What is `int (sin sqrtx)/(sqrtx) dx` equal to ?

Options

A. `(cos sqrtx)/(2) + C`
B. `2 cos sqrtx + C`
C. `(-cos sqrtx)/(2) + C`
D. `-2 cos sqrtx + C`

Answer

D

Explanation

Let `I = int (sin sqrtx)/(sqrtx) dx`
Put `sqrtx = t rArr (1)/(2 sqrtx) dx = dt rArr (1)/(sqrtx) dx = 2dt`
`:. I = 2 int sin t dt = - 2 cos t + C = - 2 cos sqrtx + C`
where 'C' is a constant of integration